Nuprl Lemma : assert_of_eq_atom
∀[x,y:Atom]. uiff(↑x =a y;x = y ∈ Atom)
Proof
Definitions occuring in Statement :
assert: ↑b,
eq_atom: x =a y,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
atom: Atom,
equal: s = t ∈ T
Definitions unfolded in proof :
eq_atom: x =a y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
all: ∀x:A. B[x],
bool: 𝔹,
true: True,
subtype_rel: A ⊆r B,
bfalse: ff,
or: P ∨ Q,
decidable: Dec(P),
btrue: tt
Lemmas referenced :
assert_wf,
btrue_wf,
bfalse_wf,
bool_wf,
true_wf,
false_wf,
equal_wf,
equal-wf-base,
atom_subtype_base,
decidable__atom_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
hypothesis,
Error :universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atom_eqEquality,
hypothesisEquality,
lambdaFormation,
unionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
dependent_functionElimination,
independent_functionElimination,
atomEquality,
applyEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
Error :inhabitedIsType,
atom_eqReduceFalseSq,
natural_numberEquality,
atom_eqReduceTrueSq
Latex:
\mforall{}[x,y:Atom]. uiff(\muparrow{}x =a y;x = y)
Date html generated:
2019_06_20-AM-11_20_28
Last ObjectModification:
2018_09_26-AM-10_50_26
Theory : atom_1
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